
The chemical potential \(\mu _k\)  in (REF ) can be roughly approximated in terms of the open-circuit potentials \(U_k\)  in the corresponding domain \(k \in \lbrace \text{n,p}\rbrace \)  as \(\mu _k = -F U_{k}\) , where \(F\)  is the Faraday constant. For the Cahn–Hilliard regular solution model [1]}, [2]}, [3]}, the chemical potential can be represented as
\(\mu _k = k_B T \ln \left( \frac{c_k}{c_k^{\max } - c_k} \right) + H \left(\frac{c_k^{\max } - 2c_k}{c_k^{\max }} \right) - \frac{\omega }{(c_k^{\max })^2} \nabla ^2 c_k,\) 
